2 citations · 4 across the 7 of their papers we have counts for
7 papers
Stability and Perron's method for Monge solutions of eikonal equations in metric spaces
Qing Liu, Made Benny Prasetya Wiranata
The main result of this paper concerns the stability of Monge solutions to eikonal equations in metric spaces. Although the subslope used in the standard definition of Monge soluti…
Superposition Property in Disjoint Variables for the Infinity Laplace Equation
Qing Liu, Juan J. Manfredi, Xiaodan Zhou
We establish a superposition principle in disjoint variables for the inhomogeneous infinity-Laplace equation. We show that the sum of viscosity solutions of the inhomogeneous infin…
Monge solutions of time-dependent Hamilton-Jacobi equations in metric spaces
Qing Liu, Made Benny Prasetya Wiranata
As a classical notion equivalent to viscosity solutions, Monge solutions are well understood for stationary Hamilton-Jacobi equations in Euclidean spaces and have been recently stu…
A parabolic PDE-based approach to Borell--Brascamp--Lieb inequality
Kazuhiro Ishige, Qing Liu, Paolo Salani
In this paper, we provide a new PDE proof for the celebrated Borell--Brascamp--Lieb inequality. Our approach reveals a deep connection between the Borell--Brascamp--Lieb inequality…
Horizontal semiconcavity for the square of Carnot-Carathéodory distance on step 2 Carnot groups and applications to Hamilton-Jacobi equations
Federica Dragoni, Qing Liu, Ye Zhang
We show that the square of Carnot-Carathéodory distance from the origin, in step 2 Carnot groups, enjoys the horizontal semiconcavity (h-semiconcavity) everywhere in the group incl…
A second-order operator for horizontal quasiconvexity in the Heisenberg group and application to convexity preserving for horizontal curvature flow
Antoni Kijowski, Qing Liu, Ye Zhang +1
This paper is concerned with a PDE approach to horizontally quasiconvex (h-quasiconvex) functions in the Heisenberg group based on a nonlinear second order elliptic operator. We di…
A representation formula for viscosity solutions of nonlocal Hamilton--Jacobi equations and applications
Takashi Kagaya, Qing Liu, Hiroyoshi Mitake
This paper is concerned with geometric motion of a closed surface whose velocity depends on a nonlocal quantity of the enclosed region. Using the level set formulation, we study a…